In all, 39 women gathered in the state reception room of Áras an Uachtaráin yesterday where they were each welcomed by the President and hugged by his wife, Sabina.
Mr Higgins said he hoped their visit was an important milestone in a long and difficult journey.
“As President of Ireland I acknowledge this point in your journey — your bravery and commitment and I am pleased that the justice of your cause has led to the public acknowledgement of the enormous wrong that you suffered at the hands of this State.”
He said the story of the Magdalene Laundries went unheard for many years and was the subject of an unacceptable silence in an area of human rights.
“That story was a story of a terrible wrong; a failure to recognise and to respect the dignity and human rights of some 10,000 women and girls who, over a period of 70 years, were placed in the Magdalene Laundries.
“That failure has now been recognised by a state and society who once were willing to look the other way,” he said.
Mr Higgins said their story had caused important questions to be asked so as to ensure such mistakes were never repeated.
His wish for the women was that they continued on their paths through life with a sense of peace and resolution and a reassuring knowledge that a society that once let them so badly had now embraced them.
The meeting with President Higgins was organised by Magdalene Survivors Together which has succeeded in its bid to have a memorial garden or museum erected in Dublin to honour women who survived the laundries.
The group’s spokesperson Steven O’Riordan, said that the memorial or garden would be situated at Sean McDermott Street where the last known Magdalene Laundry operated until 1996.
Mr O’Riordan described their visit to the Áras as a phenomenal achievement for a group of women who never thought they would be standing in the state reception room, let alone hear an apology from the Taoiseach, Enda Kenny.
Magdalene Survivors Together was established in 2009 after Mr O’Riordan’s hugely successful documentary — The Forgotten Maggies, was televised.
One of the survivors who met President Higgins yesterday was Kathleen Legg who travelled from Britain for the occasion.
“While I missed the official apology given by Enda Kenny, I was determined not to miss this. This is a great day for me as I’ll be turning 80 this year,” she said.
Another survivor, Mary Smyth, who spent time in a Magdalene laundry in Cork, said the group would continue to exist.
“The story of the Magdalene women will live on forever,” she said.